Problem No.

Extend the circular arc to point E so that angle CAE is 90º. Draw lines BE and CD.

Because angle CDE subtends the arc ED from a point on the circle it is one-half the
angle CAE at the center of the circle, or +5º, no matter where point D is. That makes
angle BDC 135º, no matter where point D is. DH is maximum when point H is at the
midpoint of BC.